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<span style="color: #800000; font-weight: normal;">\parindent</span> = 0 pt<br />
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<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">document</span></span><span style="color: #E02020; ">}</span><br />
<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">center</span></span><span style="color: #E02020; ">}</span><br />
<span style="color: #800000; font-weight: normal;">\bf</span> Laboratorio de M<span style="color: #E02020; ">\</span>'etodos Num<span style="color: #E02020; ">\</span>'ericos - Primer cuatrimestre 2012 <span style="color: #E02020; ">\\[</span><span style="color: #C08020; font-weight: normal;">5pt</span><span style="color: #E02020; ">]</span><br />
<span style="color: #800000; font-weight: normal;">\bf</span> Trabajo Pr<span style="color: #E02020; ">\</span>'actico N<span style="color: #E02020; ">\</span>'umero 3 <span style="color: #2C922C; font-style: italic;">%Cuando pase el temblor ... \\</span><br />
<span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">center</span></span><span style="color: #E02020; ">}</span><br />
<br />
<span style="color: #800000; font-weight: normal;">\vskip</span> 25pt<br />
<span style="color: #800000; font-weight: normal;">\hrule</span><br />
<span style="color: #800000; font-weight: normal;">\vskip</span> 11pt<br />
<br />
El trabajo pr<span style="color: #E02020; ">\</span>'actico consiste en evaluar la resistencia s<span style="color: #E02020; ">\</span>'<span style="color: #800000; font-weight: normal;">\i</span> smica de un<br />
edificio de varios pisos que funciona como estacionamiento, proponiendo un plan de<br />
reubicaci<span style="color: #E02020; ">\</span>'on de los veh<span style="color: #E02020; ">\</span>'iculos lo m<span style="color: #E02020; ">\</span>'as eficiente posible.<br />
<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">figure</span></span><span style="color: #E02020; ">}[</span><span style="color: #C08020; font-weight: normal;">h</span><span style="color: #E02020; ">]</span><br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Ccentering"><span style="color: #800000;">centering</span></a><br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cincludegraphics"><span style="color: #800000;">includegraphics</span></a><span style="color: #E02020; ">[</span><span style="color: #C08020; font-weight: normal;">height=0.25<span style="color: #800000; font-weight: normal;">\textheight</span></span><span style="color: #E02020; ">]{</span><span style="color: #2020C0; font-weight: normal;">figura1.eps</span><span style="color: #E02020; ">}</span><br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Ccaption"><span style="color: #800000;">caption</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">Modelo del edificio</span><span style="color: #E02020; ">}</span><br />
<span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">figure</span></span><span style="color: #E02020; ">}</span><br />
<br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Ctextbf"><span style="color: #800000;">textbf</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">El modelo</span><span style="color: #E02020; ">}</span><br />
<br />
Consideremos un edificio de <span style="color: #8020E0; font-weight: normal;">$n$</span> pisos como el de la Figura~1. Un modelo sencillo<br />
para estudiar el efecto de un terremoto sobre el edificio consiste en<br />
considerar cada piso <span style="color: #8020E0; font-weight: normal;">$i=1,<span style="color: #800000; font-weight: normal;">\dots</span>,n$</span> como un bloque de masa <span style="color: #8020E0; font-weight: normal;">$m_i$</span>, unido a los<br />
pisos adyacentes por medio de un conector el<span style="color: #E02020; ">\</span>'astico cuya acci<span style="color: #E02020; ">\</span>'on se parece<br />
a la de un resorte. Para <span style="color: #8020E0; font-weight: normal;">$i=0,<span style="color: #800000; font-weight: normal;">\dots</span>,n-1$</span>, la uni<span style="color: #E02020; ">\</span>'on entre los pisos <span style="color: #8020E0; font-weight: normal;">$i$</span> e<br />
<span style="color: #8020E0; font-weight: normal;">$i+1$</span> suministra una fuerza de restituci<span style="color: #E02020; ">\</span>'on<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">displaymath</span></span><span style="color: #E02020; ">}</span><span style="color: #8020E0; font-weight: normal;"><br />
F_i<span style="color: #E02020; ">\</span> =<span style="color: #E02020; ">\</span> k_i (x_<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">i+1</span><span style="color: #E02020; ">}</span>-x_i),<br />
</span><span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">displaymath</span></span><span style="color: #E02020; ">}</span><br />
donde <span style="color: #8020E0; font-weight: normal;">$x_i(t)<span style="color: #800000; font-weight: normal;">\colon</span> <span style="color: #800000; font-weight: normal;">\mathbb</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">R</span><span style="color: #E02020; ">}</span>_+ <span style="color: #800000; font-weight: normal;">\rightarrow</span> <span style="color: #800000; font-weight: normal;">\mathbb</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">R</span><span style="color: #E02020; ">}</span>$</span> representa el desplazamiento<br />
horizontal del <span style="color: #8020E0; font-weight: normal;">$i$</span>-<span style="color: #E02020; ">\</span>'esimo piso en cada instante con respecto al suelo (asumimos que <span style="color: #8020E0; font-weight: normal;">$i=0$</span> corresponde<br />
al suelo y que <span style="color: #8020E0; font-weight: normal;">$x_0=0$</span>), y los <span style="color: #8020E0; font-weight: normal;">$k_i<span style="color: #800000; font-weight: normal;">\in</span><span style="color: #800000; font-weight: normal;">\mathbb</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">R</span><span style="color: #E02020; ">}</span>_+$</span> representan los coeficientes<br />
de rigidez. Aplicando la segunda ley de Newton del movimiento <span style="color: #2C922C; font-style: italic;">%$F = ma$ </span><br />
a cada secci<span style="color: #E02020; ">\</span>'on del edificio (<span style="color: #8020E0; font-weight: normal;">$m_i\, a_i = F_i+F_{<span style="color: #2020C0; font-weight: normal;">i-1</span><span style="color: #E02020; ">}</span>$</span>, con <span style="color: #8020E0; font-weight: normal;">$a_i$</span> la aceleraci<span style="color: #E02020; ">\</span>'on, que escribiremos como la derivada segunda de <span style="color: #8020E0; font-weight: normal;">$x_i$</span>), <br />
obtenemos el siguiente sistema de ecuaciones diferenciales ordinarias:<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">eqnarray*</span></span><span style="color: #E02020; ">}</span><br />
m_1 <span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>_1 <span style="color: #E02020; ">&amp;</span> = <span style="color: #E02020; ">&amp;</span> -k_0 x_1 + k_1 (x_2-x_1) <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
m_2 <span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>_2 <span style="color: #E02020; ">&amp;</span> = <span style="color: #E02020; ">&amp;</span> -k_1 (x_2-x_1) + k_2 (x_3-x_2) <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
m_3 <span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>_3 <span style="color: #E02020; ">&amp;</span> = <span style="color: #E02020; ">&amp;</span> -k_2 (x_3-x_2) + k_3 (x_4-x_3) <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
<span style="color: #800000; font-weight: normal;">\vdots</span> <span style="color: #E02020; ">&amp;</span> &nbsp;<span style="color: #E02020; ">&amp;</span> <span style="color: #800000; font-weight: normal;">\vdots</span> <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
m_n <span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>_n <span style="color: #E02020; ">&amp;</span> = <span style="color: #E02020; ">&amp;</span> -k_<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">n-1</span><span style="color: #E02020; ">}</span> (x_n-x_<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">n-1</span><span style="color: #E02020; ">}</span>) <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
<span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">eqnarray*</span></span><span style="color: #E02020; ">}</span><br />
Escrito en forma matricial, este<br />
sistema toma la forma <span style="color: #8020E0; font-weight: normal;">$M<span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\mathbf</span><span style="color: #E02020; ">{</span>x</span><span style="color: #E02020; ">}}</span> = K<span style="color: #800000; font-weight: normal;">\mathbf</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>$</span>, <br />
donde <span style="color: #8020E0; font-weight: normal;">$M<span style="color: #800000; font-weight: normal;">\in</span><span style="color: #800000; font-weight: normal;">\mathbb</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">R</span><span style="color: #E02020; ">}</span>^<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">n<span style="color: #800000; font-weight: normal;">\times</span> n</span><span style="color: #E02020; ">}</span>$</span> es una matriz<br />
diagonal con las masas de los pisos y <span style="color: #8020E0; font-weight: normal;">$K<span style="color: #800000; font-weight: normal;">\in</span><span style="color: #800000; font-weight: normal;">\mathbb</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">R</span><span style="color: #E02020; ">}</span>^<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">n<span style="color: #800000; font-weight: normal;">\times</span> n</span><span style="color: #E02020; ">}</span>$</span> es una matriz<br />
tridiagonal con los coeficientes de rigidez adecuados. Como <span style="color: #8020E0; font-weight: normal;">$m_i&gt;0$</span> para<br />
<span style="color: #8020E0; font-weight: normal;">$i=1,<span style="color: #800000; font-weight: normal;">\dots</span>,n$</span>, entonces <span style="color: #8020E0; font-weight: normal;">$M$</span> tiene inversa y el sistema se puede reescribir<br />
como <span style="color: #8020E0; font-weight: normal;">$<span style="color: #800000; font-weight: normal;">\ddot</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\mathbf</span><span style="color: #E02020; ">{</span>x</span><span style="color: #E02020; ">}}</span> = (M^<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">-1</span><span style="color: #E02020; ">}</span> K) <span style="color: #800000; font-weight: normal;">\mathbf</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span> = A<span style="color: #800000; font-weight: normal;">\mathbf</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">x</span><span style="color: #E02020; ">}</span>$</span>, donde <span style="color: #8020E0; font-weight: normal;">$A = M^{<span style="color: #2020C0; font-weight: normal;">-1</span><span style="color: #E02020; ">}</span> K$</span> tiene autovalores negativos.<br />
<br />
Sean <span style="color: #8020E0; font-weight: normal;">$<span style="color: #800000; font-weight: normal;">\lambda</span>_1,<span style="color: #800000; font-weight: normal;">\dots</span>,<span style="color: #800000; font-weight: normal;">\lambda</span>_n$</span> los autovalores de <span style="color: #8020E0; font-weight: normal;">$A$</span>. Los valores<br />
<span style="color: #8020E0; font-weight: normal;">$<span style="color: #800000; font-weight: normal;">\omega</span>_i=<span style="color: #800000; font-weight: normal;">\sqrt</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">-<span style="color: #800000; font-weight: normal;">\lambda</span>_i</span><span style="color: #E02020; ">}</span>$</span>, para <span style="color: #8020E0; font-weight: normal;">$i=1,<span style="color: #800000; font-weight: normal;">\dots</span>,n$</span>, representan las frecuencias<br />
naturales del sistema, e indican la estabilidad del edificio durante un<br />
terremoto. Si la frecuencia del sismo es muy pr<span style="color: #E02020; ">\</span>'oxima a alguna de estas<br />
frecuencias, hay riesgo de que el edificio entre en resonancia y colapse.<br />
<br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Ctextbf"><span style="color: #800000;">textbf</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">El problema</span><span style="color: #E02020; ">}</span><br />
<br />
Nos encontramos en el <br />
estacionamiento de una importante concesionaria de autom<span style="color: #E02020; ">\</span>' oviles de una reconocida marca,<br />
<span style="color: #2C922C; font-style: italic;">% dep\'osito de lavarropas de una conocida casa de electrodom\'esticos, </span><br />
y se avecina un terremoto sobre nuestra ciudad. <br />
Contamos con informaci<span style="color: #E02020; ">\</span>'on fidedigna provista por nuestro<br />
informante en el Departamento de Geolog<span style="color: #E02020; ">\</span>'<span style="color: #800000; font-weight: normal;">\i</span> a de la FCEyN <br />
de que la frecuencia del terremoto ser<span style="color: #E02020; ">\</span>'a <span style="color: #8020E0; font-weight: normal;">$<span style="color: #800000; font-weight: normal;">\omega</span> = 3<span style="color: #E02020; ">\</span> <span style="color: #800000; font-weight: normal;">\hbox</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">Hz</span><span style="color: #E02020; ">}</span><br />
= 3 <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cfrac"><span style="color: #800000;">frac</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">1</span><span style="color: #E02020; ">}{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\hbox</span><span style="color: #E02020; ">{</span>seg</span><span style="color: #E02020; ">}}</span>$</span>.<br />
<br />
Para realizar c<span style="color: #E02020; ">\</span>'alculos simplificados podemos asumir que todos los autos <br />
se pueden agrupar en 2 categor<span style="color: #E02020; ">\</span>'ias: livianos, de masa <span style="color: #8020E0; font-weight: normal;">$m_l$</span>, y pesados, <br />
de masa <span style="color: #8020E0; font-weight: normal;">$m_p &gt; m_l$</span>.<br />
Adem<span style="color: #E02020; ">\</span>'as, <span style="color: #8020E0; font-weight: normal;">$m_0$</span> es la masa propia del edificio correspondiente a cada piso.<br />
De esta forma, si el piso <span style="color: #8020E0; font-weight: normal;">$i$</span> tiene <span style="color: #8020E0; font-weight: normal;">$l_i$</span> veh<span style="color: #E02020; ">\</span>'<span style="color: #800000; font-weight: normal;">\i</span> culos livianos y <br />
<span style="color: #8020E0; font-weight: normal;">$p_i$</span> veh<span style="color: #E02020; ">\</span>'<span style="color: #800000; font-weight: normal;">\i</span> culos pesados, entonces su masa es <span style="color: #8020E0; font-weight: normal;">$m_i = m_0 + l_i m_l + p_i m_p$</span>. <br />
El problema que debemos resolver -y r<span style="color: #E02020; ">\</span>'apidamente- consiste en determinar<br />
cu<span style="color: #E02020; ">\</span>'antos autos livianos y pesados debemos quitar de cada piso <br />
(reubic<span style="color: #E02020; ">\</span>'andolos en otros pisos) para que ninguna de las frecuencias <br />
naturales del edificio se encuentre a menos del 10<span style="color: #800000; font-weight: normal;">\%</span> de la frecuencia <br />
<span style="color: #8020E0; font-weight: normal;">$<span style="color: #800000; font-weight: normal;">\omega</span>$</span> del terremoto.<br />
La soluci<span style="color: #E02020; ">\</span>'on <span style="color: #E02020; ">\</span>'optima del problema es aquella que permite evitar que el<br />
edificio colapse, reubicando la menor cantidad posible de autom<span style="color: #E02020; ">\</span>'oviles.<br />
<br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Ctextbf"><span style="color: #800000;">textbf</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">El enunciado</span><span style="color: #E02020; ">}</span><br />
<br />
El trabajo pr<span style="color: #E02020; ">\</span>'actico consiste en implementar un programa que permita <br />
resolver este problema. La soluci<span style="color: #E02020; ">\</span>'on propuesta debe indicar cu<span style="color: #E02020; ">\</span>'antos <br />
autos livianos y cu<span style="color: #E02020; ">\</span>'antos pesados quitar de cada piso, y a qu<span style="color: #E02020; ">\</span>'e pisos <br />
se deben llevarlos. <br />
<br />
Deben proponerse (por lo menos) dos m<span style="color: #E02020; ">\</span>'etodos (es v<span style="color: #E02020; ">\</span>'alido que sean <br />
heur<span style="color: #E02020; ">\</span>'<span style="color: #800000; font-weight: normal;">\i</span> sticos) para obtener el plan de reubicaci<span style="color: #E02020; ">\</span>'on. El informe <br />
deber<span style="color: #E02020; ">\</span>'a contener los resultados de los experimentos realizados para<br />
compararlos y evaluar cu<span style="color: #E02020; ">\</span>'al es mejor. <br />
<br />
El programa debe incluir una implementaci<span style="color: #E02020; ">\</span>'on de<br />
alg<span style="color: #E02020; ">\</span>'un algoritmo para calcular los autovalores de una matriz cuadrada, que<br />
deber<span style="color: #E02020; ">\</span>'a ser utilizado durante el proceso de decisi<span style="color: #E02020; ">\</span>'on. Sugerimos implementar<br />
el algoritmo QR para el c<span style="color: #E02020; ">\</span>'alculo de autovalores. El programa debe tomar los<br />
datos desde un archivo de texto con el siguiente formato:<br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">eqnarray</span></span><span style="color: #E02020; ">}</span><span style="color: #8020E0; font-weight: normal;"><br />
&nbsp;<span style="color: #E02020; ">&amp;</span> <span style="color: #E02020; ">&amp;</span> n<span style="color: #E02020; ">\</span> m_0<span style="color: #E02020; ">\</span> m_l<span style="color: #E02020; ">\</span> m_p <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
&nbsp;<span style="color: #E02020; ">&amp;</span> <span style="color: #E02020; ">&amp;</span> k_0<span style="color: #E02020; ">\</span> k_1<span style="color: #E02020; ">\</span> <span style="color: #800000; font-weight: normal;">\dots</span><span style="color: #E02020; ">\</span> k_<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">n-1</span><span style="color: #E02020; ">}</span> <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
&nbsp;<span style="color: #E02020; ">&amp;</span> <span style="color: #E02020; ">&amp;</span> l_1<span style="color: #E02020; ">\</span> l_2<span style="color: #E02020; ">\</span> <span style="color: #800000; font-weight: normal;">\dots</span><span style="color: #E02020; ">\</span> l_n <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a> <span style="color: #E02020; ">\\</span><br />
&nbsp;<span style="color: #E02020; ">&amp;</span> <span style="color: #E02020; ">&amp;</span> p_1<span style="color: #E02020; ">\</span> p_2<span style="color: #E02020; ">\</span> <span style="color: #800000; font-weight: normal;">\dots</span><span style="color: #E02020; ">\</span> p_n <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cnonumber"><span style="color: #800000;">nonumber</span></a><br />
</span><span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">eqnarray</span></span><span style="color: #E02020; ">}</span><br />
Se debe retornar la soluci<span style="color: #E02020; ">\</span>'on propuesta con este mismo formato.<br />
<br />
El programa que obtenga la mejor redistribuci<span style="color: #E02020; ">\</span>'on de autom<span style="color: #E02020; ">\</span>'oviles se har<span style="color: #E02020; ">\</span>'a<br />
acreedor a la medalla <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cemph"><span style="color: #800000;">emph</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">M\'etodos Num\'ericos 2012</span><span style="color: #E02020; ">}</span> al Mejor Redistribuidor Vehicular.<br />
<br />
<span style="color: #800000; font-weight: normal;">\vskip</span> 15pt<br />
<br />
<span style="color: #800000; font-weight: normal;">\hrule</span><br />
<br />
<span style="color: #800000; font-weight: normal;">\vskip</span> 11pt<br />
<br />
<br />
<span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\bf</span> <span style="color: #800000; font-weight: normal;">\underline</span><span style="color: #E02020; ">{</span>Entrega Final</span><span style="color: #E02020; ">}}</span><br />
<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Cvspace"><span style="color: #800000;">vspace</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">-15pt</span><span style="color: #E02020; ">}</span><br />
<span style="color: #C00000; font-weight: normal;">\begin</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">description</span></span><span style="color: #E02020; ">}</span><br />
&nbsp; <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Csetlength"><span style="color: #800000;">setlength</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\itemsep</span></span><span style="color: #E02020; ">}{</span><span style="color: #2020C0; font-weight: normal;">0pt</span><span style="color: #E02020; ">}</span><br />
&nbsp; <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Csetlength"><span style="color: #800000;">setlength</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">\<a href="http://www.golatex.de/wiki/index.php?title=%5Cparskip"><span style="color: #800000;">parskip</span></a></span><span style="color: #E02020; ">}{</span><span style="color: #2020C0; font-weight: normal;">0pt</span><span style="color: #E02020; ">}</span><br />
&nbsp; <span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Csetlength"><span style="color: #800000;">setlength</span></a><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #800000; font-weight: normal;">\parsep</span></span><span style="color: #E02020; ">}{</span><span style="color: #2020C0; font-weight: normal;">0pt</span><span style="color: #E02020; ">}</span><br />
&nbsp;<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Citem"><span style="color: #800000;">item</span></a><span style="color: #E02020; ">[</span><span style="color: #C08020; font-weight: normal;">Formato Electr\'onico:</span><span style="color: #E02020; ">]</span> jueves 28 de junio de 2012, hasta las 23:59 hs, a la direcci<span style="color: #E02020; ">\</span>'on: <br />
<br />
&nbsp; <span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;">\<a href="http://www.golatex.de/wiki/index.php?title=%5Cemph"><span style="color: #800000;">emph</span></a><span style="color: #E02020; ">{</span>metnum.lab@gmail.com</span><span style="color: #E02020; ">}}</span><br />
<span style="color: #2C922C; font-style: italic;">% &nbsp;\item[Formato f\'isico y experimentación en clase:] 13 de abril de 2012, de 17 a 21 hs.</span><br />
&nbsp;<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Citem"><span style="color: #800000;">item</span></a><span style="color: #E02020; ">[</span><span style="color: #C08020; font-weight: normal;">Formato f\'isico:</span><span style="color: #E02020; ">]</span> viernes 29 de junio de 2012, de 17 a 19 hs.<br />
&nbsp;<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Citem"><span style="color: #800000;">item</span></a><span style="color: #E02020; ">[</span><span style="color: #C08020; font-weight: normal;">Competencia entre grupos:</span><span style="color: #E02020; ">]</span> viernes 29 de junio de 2012, 19 hs.<br />
&nbsp;<span style="color: #E02020; ">\</span><a href="http://www.golatex.de/wiki/index.php?title=%5Citem"><span style="color: #800000;">item</span></a><span style="color: #E02020; ">[</span><span style="color: #C08020; font-weight: normal;">Entrega de premios:</span><span style="color: #E02020; ">]</span> viernes 29 de junio de 2012, 20:30 hs.<br />
<span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">description</span></span><span style="color: #E02020; ">}</span><br />
<br />
<br />
<span style="color: #C00000; font-weight: normal;">\end</span><span style="color: #E02020; ">{</span><span style="color: #2020C0; font-weight: normal;"><span style="color: #0000D0; font-weight: normal;">document</span></span><span style="color: #E02020; ">}</span><br />
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